Here we will explain how to simplify the cube root of 14823 (∛14823). We start by labeling the parts of ∛14823 so it is easy to follow along:
∛14823 = 1∛14823 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 14823 in its simplest form means that you want the radicand to be as small as possible and the coefficient of the radical to be as large as possible.
To simplify the cube root of 14823, we first find the greatest perfect cube from the list of factors of 14823. The factors of 14823 are 1, 3, 9, 27, 61, 81, 183, 243, 549, 1647, 4941, and 14823.
Any number multiplied by itself three times will make a perfect cube. The greatest perfect cube from the list of factors above is 27 (3 times 3 times 3 equals 27).
To find the simplified radicand (r) in the cube root of 14823, we divide 14823 by 27, which gives us 549.
To find the simplified coefficient of the radical (c) in the cube root of 14823, we take the cube root of 27, which gives us 3.
That is how you simplify the cube root of 14823. Therefore, the cube root of 14823 in its simplest radical form is as follows:
∛14823 = 3∛549
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